Re: Gaussian dist. Integral

[John Denker <jsd@MONMOUTH.COM>]

At 08:47 PM 5/11/99 -0700, Mike Wilson wrote:
> I have never worked out the integral which results in the normal or
> gaussian distribution equation (about .4 e^(-.5 z^2) , where z is defined
> in terms of the population mean and standard deviation).
> I usually just work off compiled tables.
>
> Can someone in the list point me to a source which explains the
> integral and initial equation needed to derive the equation.

It's in Feynman somewhere.  The trick is this:

Let
        I    = integral exp (- x**2) dx
then rather than calculating I directly, calculate I**2.
        I**2 = integral integral exp (- x**2 - y**2) dx dy
then switch to polar coordinates and find an easy-to-do integral.

-- jsd